The German auto maker needs to fix the famously inefficient operation that makes Volkswagen-branded cars at home in Wolfsburg

One of the mysteries of Volkswagen is how one of the world’s most profitable car makers can coexist with one of the least profitable in the same corporate entity.

Matthias Müller, chief executive since the emissions scandal broke last September, used to run Porsche, a division of the Volkswagen group since 2011. If he can bring the kind of discipline Porsche is showing to the entire company—notably the famously inefficient operation that makes Volkswagen-branded cars in Wolfsburg, North Germany—investors wouldn’t need to...